BRPI0712982A2 - method for employing sec-ftir data to predict mechanical properties of polyethylene - Google Patents

Abstract

METHOD FOR USING SEC-FTIR DATA TO PREVENT MECHANICAL POLYETHYLENE PROPERTIES. The present invention provides various methods for determining physical and chemical property values of polymers. In these methods, at least two polymeric training samples are provided. The characteristics of the polymeric microstructures of the training samples are correlated to the physical or chemical property values of the training samples. These correlations are then applied to the respective characteristics of polymeric test samples to determine the physical or chemical property values of the test samples.

Description

METHOD FOR USING SEC-FTIR DATA TO PREVENT MECHANICAL POLYETHYLENE PROPERTIES

BACKGROUND OF THE INVENTION

The present invention is directed to methods for determining physical and chemical property values of polymers. Traditionally, in order to determine a value of a specific physical or chemical property, a certain amount of the particular polymeric resin was required to make a test article or specimen, and then the resulting test article or specimen was subsequently tested through analytical tests to determine the value of the physical or chemical property. This procedure is tedious not only because of the time required to manufacture the test article or specimen, but also because of the time required to perform the respective analytical test procedure. Moreover, the traditional method, depending on the particular test, could require large amounts of polymer, often more than could be produced in a small-scale research laboratory or pilot installation device.

Accordingly there is a need for a method to determine a desired chemical or physical property value of a test sample that requires only a small amount of polymer for analysis. In addition, this method should prepare the physical or chemical property value of the test sample to be determined without the manufacture of a test article or specimen. Further, this method should allow the determination of the physical or chemical property value of the test sample without performing analytical testing for physical or chemical property.

In another aspect, there is a need for a method to quickly determine a value of a desired chemical or physical property of a test sample. It is beneficial to determine the value of chemical or physical property without having to invest the time and money required to manufacture test articles or specimens for further analysis, nor invest the time and money required to perform the analytical test procedure which, depending on the specific test. , it may take days or weeks to determine the value of the respective property. The resin design and product development cycle time to achieve a desired physical or chemical property attribute could be greatly reduced with a method that provides rapid response using only a small amount of a polymeric test sample. Accordingly, the methods of the present invention are directed to the above.

BRIEF SUMMARY OF THE INVENTION

The present invention discloses a method for determining physical and chemical property values of polymers. In one aspect, the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample. The at least one polymeric test sample has a molecular weight distribution profile (MWD) and a short chain branch distribution (SCBD). In this regard, the method for determining a physical or chemical property value of at least one polymeric test sample comprises: a) providing at least two training samples, each training sample having a MWD profile, a SCBD and a known value. the respective physical or chemical property;

b) determining at least two cross-weighted terms at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each weighted cross-term being determined as the product of the multiplication of:

(1) the respective molecular weight;

(2) the weight fraction of the respective molecular weight; and

(3) the number of short chain branches per 1,000 carbon atoms at the respective molecular weight;

c) marking each weighted cross-term versus molecular weight logarithm for each of at least two polymer training samples and at least one polymeric test sample;

d) determining the respective area under each curve in step (c);

e) correlating the respective areas for each of at least two polymer training samples in step (d) with the known value of the respective physical or chemical property; and

f) applying the correlation of step (e) to the respective area of at least one polymeric test sample to determine the physical or chemical property value of at least one polymeric test sample.

In another aspect of the present invention, the method is directed to single point determination. That is, the weighted crossover term is determined at a single molecular weight. In this regard, the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample. The at least one polymeric test sample has a molecular weight, a weight fraction at the respective molecular weight and a number of short chain branches per 1,000 carbon atoms at the respective molecular weight. This method comprises:

(a) provide at least two polymeric training samples, each training sample having a molecular weight, a weight fraction at its molecular weight, a number of short chain branches per 1,000 carbon atoms at its molecular weight, and a known value of their physical or chemical property.

(b) determine a cross-term weighted by molecular weight for each of at least two polymeric training samples and at least one polymeric test sample, each weighted cross-term being determined as the product of multiplication of:

(1) the respective molecular weight;

(2) the weight fraction of the respective molecular weight; and

(3) the number of short chain branches per 1,000 carbon atoms at the respective molecular weight;

c) correlating the respective weighted cross terms for each of at least two polymer training samples in step (b) with the known value of the respective physical or chemical property; and d) applying the correlation of step (c) to the weighted cross-term of at least one polymeric test sample to determine the physical or chemical property value of at least one polymeric test sample.

In yet another aspect of the present invention, a chemometric method may be used to determine a physical or chemical property value of at least one polymeric test sample. At least one polymeric test sample has a MWD profile and an SCBD. This method comprises:

(a) provide at least two training samples, each training sample having a MWD profile, an SCBD and a known value of the respective physical or chemical property;

b) determining at least two cross-weighted terms at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each weighted cross-term being determined as the product of the multiplication of:

(1) the respective molecular weight;

(2) the weight fraction of the respective molecular weight; and

(3) the number of short chain branches per 1,000 carbon atoms at the respective molecular weight;

c) by chemometric analysis, define a mathematical relationship between the values of the respective physical or chemical property and the weighted cross terms for each of at least two polymeric training samples; and d) applying the mathematical relationship of step (c) to the respective weighted cross-terms of step (b) for at least one polymeric test sample to determine the physical or chemical property value of at least one polymeric test sample.

In a different aspect, the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample using probabilities of entangled molecules. For example, at least one polymeric test sample has a composite density, a MWD profile and an SCBD. The method for determining a physical or chemical property value of at least one polymeric test sample comprises:

(a) provide at least two training samples, each training sample having a composite density, a MWD profile, an SCBD and a known value of the respective physical or chemical property;

b) determining at least two terms of density at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each density term. being determined using composite density, MWD profile and SCBD;

c) determining a respective melting temperature from each density term in step (b);

d) determining a respective probability for intertwined molecule formation from each melting temperature in step (c); e) determining a respective weighted interlaced molecule probability, each weighted interlaced molecule probability being determined as the product of the multiplication of:

(1) the weight fraction of the respective molecular weight; and

(2) the probability for formation of entangled molecule in step (d) at the respective molecular weight;

f) plotting each probability of weighted entangled molecule versus molecular weight logarithm for each of at least two polymer training samples and at least one polymeric test sample;

g) determining the respective area under each curve in step (f);

h) correlating the respective areas for each of at least two polymer training samples in step (g) with the known value of the respective physical or chemical property; and

i) applying the correlation of step (h) to the respective area of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample.

A further aspect of the present invention is a single point method utilizing interlaced molecule probabilities. That is, the probability of weighted cross-linked molecule is determined at a single molecular weight. In this regard, the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample. The at least one polymeric test sample has a composite density, a molecular weight and a weight fraction at the respective molecular weight. This method comprises:

(a) provide at least two training samples, each training sample having a composite density, molecular weight, molecular weight fraction and known physical or chemical property value;

b) determining a minimum molecule length for one interlaced molecule (2LC + La) using the composite density for each of at least two polymeric training samples and at least one polymeric test sample;

c) determining a respective probability for intertwined molecule formation at the respective molecular weight from each 2LC + La of step (b);

d) determining a respective weighted interlaced molecule probability, each weighted interlaced molecule probability being determined as the product of the multiplication of:

(1) the weight fraction of the respective molecular weight; and

(2) the probability for formation of entangled molecule in step (c) at the respective molecular weight;

e) correlating the respective probability of weighted entangled molecule for each of at least two polymer training samples in step (d) with the known value of the respective physical or chemical property; and

f) applying the correlation of step (e) to the weighted entangled probability of the at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample.

DEFINITIONS

The following definitions are provided to assist those skilled in the art to understand the detailed description of the present invention.

dW / d Log M - Weight fraction.

ESCR - Environmental Stress Crack Resistance, ASTM D1693.

FNCT - Full Grooved Creep Test, ISO 16770.

FTIR - Fourier Transform Infrared Spectrophotometry.

M or MW - Molecular Weight.

MWD - Molecular Weight Distribution.

Mn - MW in numerical average.

Mw - MW in weighted average.

NDR - Natural Breath Ratio, ASTM D63 8.

NPT - Grooved Tube Test, ISO 13479.

PENT - Pennsylvania Splined Test, ASTM F1473, measured in hours.

PSP1 - Parameter 1 of the main structure; calculated by dividing the area under the weighted cross-term plot curve versus molecular weight by 100,000.

PSP2 - Parameter 2 of the main structure; calculated by multiplying the area under the weighted interlaced molecule probability plot versus molecular weight curve by 100.

pTM or P - Probability for intertwined molecule formation.

SCBD - Short Chain Branch Distribution.

SCB's - number of short chain branches per 1,000 carbon atoms.

SEC - Size Exclusion Chromatography; also called Gel Permeation Chromatography (GPC).

SP-NCTL - Single Point Grooved Constant Tensile Load, ASTM D5397, 30% yield.

Weighted Cross-Term - Product of multiplying a molecular weight, the weight fraction at the respective molecular weight and the number of short chain branches per 1,000 carbon atoms at the respective molecular weight; also shown as M * dW / d (Log M) * SCB.

Probability of Weighted Interlaced Molecule Product of weight fraction multiplication at one molecular weight and the probability for interlaced molecule formation at the respective molecular weight; also shown as dW / d (Log M) * Ptm.

2LC + La - Minimum molecule length for one interlaced molecule; Lc is the thickness of the crystalline lamella and La is the thickness of the amorphous layer.

BRIEF DESCRIPTION OF THE FIGURES

Figure 1 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for an exemplary polyolefin copolymer.

Figure 2 is a graph of the weighted cross-term versus molecular weight logarithm for an exemplary polyolefin copolymer.

Figure 3 shows a Log PENT graph (in hours) at 2.4 MPa versus primary parameter structure 1 (PSP1) for two exemplary series of polyolefin polymers.

Figure 4 presents a graph illustrating an empirical correlation of composite density versus weighted average molecular weight logarithm for an exemplary homopolymer.

Figure 5 presents a graph for the MWD profile and the respective terms of homopolymer and copolymer density across the MWD profile for an exemplary polyolefin copolymer.

Figure 6 presents a graph illustrating an empirical melt temperature versus density correlation for polyethylene polymers.

Figure 7 presents a graph of 2LC + La (measured in nm) as a density function for one aspect of a method of the present invention compared to the values reported in the literature.

Figure 8 presents a plot of the weighted interlaced molecule probability versus the molecular weight logarithm for two exemplary polyolefin copolymers.

Figure 9 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-I bimodal polyethylene polymer.

Figure 10 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-2 bimodal polyethylene polymer.

Figure 11 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-3 bimodal polyethylene polymer.

Figure 12 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-4 bimodal polyethylene polymer.

Figure 13 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-5 bimodal polyethylene polymer.

Figure 14 is a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-6 bimodal polyethylene polymer.

Figure 15 presents a graph of the molecular weight distribution profile (MWB) and short chain branching distribution (SCBD) for a BM-7 bimodal polyethylene polymer.

Figure 16 shows a weighted cross-term plot versus molecular weight logarithm for BM-I to BM-7 polyethylene polymer training samples.

Figure 17 shows a Log PENT graph (in hours) at 2.4 MPa versus PSP1 for BM-2 to BM-7 bimodal polyethylene polymer training samples.

Figure 18 shows a weighted cross-term versus molecular weight logarithm plot for polyethylene polymer training samples produced using a chromium-based catalyst.

Figure 19 shows a Log PENT (in hours) graph at 2.4 MPa versus PSPl for polyethylene copolymer training samples using a chromium-based catalyst.

Figure 20 shows a log PENT graph (in hours) at 2.4 MPa versus weighted cross-terms divided by 100,000 for bimodal polyethylene polymer training samples.

Figure 21 shows a Log PENT (in hours) graph at 2.4 MPa using chemometric versus PENT analysis measured for various polymeric polyethylene training samples.

Figure 22 shows a Log PENT (in hours) graph at 2.4 MPa using chemometric versus PENT analysis measured for various polymeric polyethylene training samples.

Figure 23 presents a Log PENT graph (in hours) at 2.4 MPa versus PSP2 for polymeric polyethylene training samples using different catalyst systems.

Figure 24 shows a Log SP-NCTL (in hours) versus PSP2 graph for polymeric polyethylene training samples using different catalyst systems.

Figure 25 shows an NDR versus PSP2 graph for polymeric polyethylene training samples using different catalyst systems.

Figure 26 shows a Log PENT graph (in hours) at 2.4 MPa versus probability of weighted interlaced molecule for bimodal polyethylene polymer training samples. DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed to a method for determining physical and chemical property values of polymers. Exemplary physical and chemical properties of interest in the present invention include, but are not limited to, PENT, ESCR, SP-NCTL, NPT, FNCT, NDR, izod impact, puncture impact, Charpy impact, puncture resistance, and tear resistance. from Elmendorf. The PENT value can be determined under different conditions such as 2.4 MPa, 3.0 MPa or 3.8 MPa.

The method of the present invention is applicable to all classes of polymers, although the method is particularly well suited to semicrystalline polymers. The invention will be described in connection with polyolefins, particularly polyethylene homopolymers and copolymers. It is understood that the present invention is not limited to the aspects and examples summarized herein, and that the present invention includes all alternatives, modifications and equivalents that may be included in the spirit and scope of the specification and claims that follow.

Differences in polymer microstructure, such as the MWD profile and SCBD of a given polymer, can influence the resulting physical and chemical properties of that polymer. Thus, in one aspect of the present invention, the method described herein can determine the physical or chemical property values of test samples using knowledge of the MWD and SCBD profile of the respective test samples. In another aspect, a method according to this invention further requires a composite resin density of the polymeric test sample. The MWD profile of a polymer may be provided by any means known to that of ordinary skill in the art. A non-limiting example of an analytical technique for determining the MWD profile of a polymer is SEC or GPC. Inherently, as used in this disclosure, the MWD profile of a polymer may provide, among other data, the MWD data and weight fractions associated with each MW, including common technical terms such as Mw and Mn.

Similarly the SCBD of a polymer may be provided by any means known to those skilled in the art. Techniques could include, but are not limited to, temperature elevation elution fractionation (TREF), nuclear magnetic resonance (NMR), and SEC-FTIR. Inherently, as used in this disclosure, a polymer SCBD can provide the number of Poe short chain branches 1,000 carbon atoms (SCB's) in each MW through the MWD profile.

One method for providing both the MWD and SCBD profiles of a polymer is SEC-FITR using chemometric analysis, described in US Patent No. 6,632,680 and US Patent Application Serial No. 10 / 463,849, the disclosure of which are incorporated herein in its entirety by this reference. An advantage of SEC-FTIR with respect to the methods of the present invention is the small amount of polymeric training samples and polymeric test samples that are required for analysis to determine the MWD and SCBD profile. In one aspect of the present invention, less than about 5 grams of each respective test or training sample is provided for PWD and SCBD profiling. In another aspect, less than about 1 gram is provided for analysis. In an additional aspect, less than about 100 milligrams are provided. In addition, another advantage of the present invention is that it readily determines a physical or chemical property of a test sample as compared to conventional tests and measurement methods. Using a technique such as SEC-FTIR in combination with the methods of the present invention, the value of a physical or chemical property can be determined in less than three hours. In another aspect, the value of a physical or chemical property can be determined in less than two hours. In yet another aspect, the value of a physical or chemical property can be determined in less than an hour.

Composite resin density may likewise be determined by any means known to those of ordinary skill in the art. Analytical techniques include, but are not limited to, ASTM D1238 refractive index or molded density. Composite resin density is the density of the polymer as a whole across all molecular weights.

While methods are described in terms of "understanding" various steps, methods may also "consist essentially of" or "consist of" various steps.

MAIN STRUCTURE PARAMETER 1 (PSPl)

One aspect of the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a molecular weight distribution (MWD) profile and a distribution of short chain branching (SCBD). MWD profile and SCBD may be determined by any analytical technique known to that of ordinary skill in the art, such as SEC-FTIR. The polymeric test sample may also be called an experimental sample or an unknown sample. The method for determining a physical or chemical property value of at least one polymeric test sample comprises:

(a) provide at least two training samples, each training sample having a MWD profile, an SCBD and a known value of the respective physical or chemical property;

b) determining at least two cross-weighted terms at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each weighted cross-term being determined as the product of the multiplication of:

(1) the respective molecular weight;

(2) the weight fraction of the respective molecular weight; and

(3) the number of short chain branches per 1,000 carbon atoms at the respective molecular weight;

c) marking each weighted cross-term versus molecular weight logarithm for each of at least two polymer training samples and at least one polymeric test sample;

d) determining the respective area under each curve in step (c);

e) correlating the respective areas for each of at least two polymer training samples in step (d) with the known value of the respective physical or chemical property; and

f) applying the correlation of step (e) to the respective area of at least one polymeric test sample to determine the physical or chemical property value of at least one polymeric test sample.

At least two polymeric training samples are provided according to the methods of the present invention. Training samples may also be referred to as control samples. Each polymeric training sample has a known MWD profile and a known SCBD. MWD profile and SCBD can be determined using a technique such as SEC-FTIR as mentioned above. For an exemplary polyolefin copolymer, Figure 1 illustrates the MWD and SCBD profile of the copolymer. The "x" axis is the logarithm of the molecular weight, the left side of the "y" axis is the weight fraction at each molecular weight, and the right side of the "y" axis is the number of short chain branches per 1,000 carbon atoms. carbon (SCB's). Graphic data, as illustrated in Figure 1, may be provided for at least two polymeric training samples and at least one polymeric test sample.

Also, each polymeric training sample has a known value of the respective physical or chemical property of interest. For example, at least two polymeric training samples may be provided, each having a known value of PENT at 2.4 MPa, the value of PENT having been previously determined using the respective analytical test for PENT.

At least two polymeric training samples are used in the methods of the present invention. Alternatively, however, at least three training samples, at least four training samples, at least five training samples, at least ten training samples, at least fifteen training samples or at least twenty training samples may be used. There is no specific upper limit on the number of different training samples that can be used with the present invention. It is beneficial that training samples resemble the polymeric test sample, and that the range covered by the training samples encompasses the polymeric test sample, although it is not required. In addition, training samples may include duplicate or redundant samples to include the impact of experimental error on MWD and SCBD profiling tests, and the physical or chemical property of interest.

For each of at least two polymeric training samples and at least one polymeric test sample, weighted cross-terms may be determined using the respective data for each sample as exemplified in Figure 1. A weighted cross-term is the product of multiplying a molecular weight, the weight fraction at the respective molecular weight and the number of short chain branches per 1,000 carbon atoms at the respective molecular weight (ie M * dW / d (Log () * SCB's). While not intended to be limited by this theory, Applicants suggest that a factor related to polymers with improved hardness (eg tear strength, impact, puncture or stress cracking) is the presence of more short chain branches at molecular weights. taller. That is, the presence of high branching levels at lower molecular weights does not significantly contribute to hardness (eg in properties such as PENT, SP-NCTL, drilling impact and the like). Particularly, a high short chain branch content present at the high molecular weight end of the MWD profile can contribute significantly to improve polymer hardness. Again, not wishing to be bound by this theory, applicants believe that the weighted crossover term, as defined above, captures the impact of having higher branch content on the higher molecular weight fraction of the polymer.

According to one aspect of the present invention, at least two cross-terms weighted at respective molecular weights along the MWD and SCBD profile are required. Each weighted cross-term is plotted versus the logarithm of its molecular weight for each of at least two polymeric training samples and at least one polymeric test sample. This is illustrated in Figure 2 for an exemplary polyolefin copolymer. Although at least two weighted cross terms are required, it is beneficial to have many more cross terms across the molecular weight range to form a curve as shown in Figure 2. Thus, according to another aspect of the present invention, at least five weighted cross terms At least ten weighted crossover terms, at least twenty-five weighted crossover terms, at least fifty weighted crossover terms or at least one hundred weighted crossover terms may be used. There is no specific upper limit on the number of weighted cross terms that may be used with the present invention. More weighted cross terms provide a smoother curve as illustrated in Figure 2.

For each of at least two polymeric training samples and at least one polymeric test sample, the area under the respective curve for each sample is determined. For example, the area under the curve of Figure 2 for the exemplary copolymer is determined. The respective areas under the curve for each of at least two polymeric training samples correlate with the respective values of the physical or chemical properties of interest. In one aspect of the present invention, the area under each curve is divided by 100,000 to calculate primary structure parameter 1 (PSP1). Figure 3 illustrates a correlation of a specific physical or chemical property (in this case, Log PENT at 2.4 MPa) versus PSP1 for two exemplary series of polyolefin polymers. The results indicate that there is a linear relationship between the logarithm of the property of interest and the value of PSP1, which is affected by the branch content of the high molecular weight fraction of the copolymer.

By applying a correlation, as illustrated in Figure 3, to the respective area under the curve of at least one polymeric test sample, the physical or chemical property value of at least one polymeric test sample can be determined. This method is further illustrated in the following Examples 1 and 2.

Another aspect of the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a molecular weight, a weight fraction at its molecular weight and a number of short chain branches per 1,000 carbon atoms in their molecular weight. These parameters can be determined from the MWD profile and the SCBD by any analytical technique known to that of common skill in the art, such as SEC-FTIR. This method for determining a physical or chemical property value of at least one polymeric test sample comprises:

(a) provide at least two polymeric training samples, each training sample having a molecular weight, a weight fraction at its molecular weight, a number of short chain branches per 1,000 carbon atoms at its molecular weight, and a known value of their physical or chemical property.

(b) determine a cross-term weighted by molecular weight for each of at least two polymeric training samples and at least one polymeric test sample, each weighted cross-term being determined as the product of multiplication of:

(1) the respective molecular weight;

(2) the weight fraction of the respective molecular weight; and (3) the number of short chain branches per -1,000 carbon atoms at the respective molecular weight;

c) correlating the respective weighted cross terms for each of at least two polymer training samples in step (b) with the known value of the respective physical or chemical property; and

d) applying the correlation of step (c) to the weighted cross-term of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample.

The above method is a single point determination of the method illustrated in Figures 1-3. In this method, a single cross-term weighted to a single molecular weight is determined for each of at least two polymeric training samples and at least one polymeric test sample. This method is further illustrated by the following Example 3.

It is apparent from Figure 3 that not all types of polymers have the same correlation between physical or chemical property and the weighted crossover term or PSP1. For example, each family of polyolefin resins produced with different catalyst systems (such as chromium, Ziegler-Natta, metallocene and the like, or combinations thereof) or with different production processes (such as semifluid mixture, solution, gas phase and the like or combinations of these) may have a different calibration curve or a different relationship to the physical or chemical property of interest.

According to a further aspect of the present invention, a chemometric method may be used to determine a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a MWD profile and a SCBD. This method comprises:

(a) provide at least two training samples, each training sample having a MWD profile, an SCBD and a known value of the respective physical or chemical property;

b) determining at least two cross-weighted terms at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each weighted cross-term being determined as the product of the multiplication of:

(1) the respective molecular weight;

(2) the weight fraction of the respective molecular weight; and

(3) the number of short chain branches per 1,000 carbon atoms at the respective molecular weight;

c) by chemometric analysis, define a mathematical relationship between the values of the respective physical or chemical property and the weighted cross terms for each of at least two polymeric training samples; and

d) applying the mathematical relationship of step (c) to the respective weighted cross-terms of step (b) for at least one polymeric test sample to determine the physical or chemical property value of at least one polymeric test sample.

This chemometric method may be used when at least two polymeric training samples and at least one polymeric test sample are prepared using catalyst systems that are identical or different. For example, this method can be used for different families of polyolefin resins produced with different catalyst systems (such as chromium, Ziegler-Natta, metallocene and the like, or combinations thereof) or with different production processes (such as semifluid mixture, solution, gas phase and the like or combinations thereof).

Chemometric analysis has also been described in U.S. Patent No. 6,632,680 and U.S. Patent Application Serial No. 10 / 463,849. In the present invention, chemometric analysis may be used to define a mathematical relationship between the values of the respective physical or chemical property and the weighted cross terms for each of at least two polymeric training samples. At least two polymeric training samples are used in this aspect of the present invention. Alternatively, however, at least three training samples, at least four training samples, at least five training samples, at least ten training samples, at least fifteen training samples or at least twenty training samples may be used. There is no specific upper limit on the number of different training samples that may be used in this aspect of the present invention. This chemometric method is further illustrated by the following Examples 4 and 5.

MAIN STRUCTURE PARAMETER (PSP2) In another aspect, the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample to at least one polymeric test sample having a density of composite, one MWD profile and one SCBD. The density of the composite may be determined by any analytical technique known to that of ordinary skill in the art as mentioned above. The method for determining a physical or chemical property value of at least one polymeric test sample comprises:

(a) provide at least two training samples, each training sample having a composite density, a MWD profile, an SCBD and a known value of the respective physical or chemical property;

b) determining at least two terms of density at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each density term. being determined using composite density, MWD profile and SCBD;

c) determining a respective melting temperature from each density term in step (b);

d) determining a respective probability for intertwined molecule formation from each melting temperature in step (c);

e) determining a probability of respective weighted entangled molecule, each probability of weighted entangled molecule being determined as the product of multiplication of: (1) the weight fraction of the respective molecular weight; and

(2) the probability for formation of entangled molecule in step (d) at the respective molecular weight;

f) plotting each probability of weighted entangled molecule versus molecular weight logarithm for each of at least two polymer training samples and at least one polymeric test sample;

g) determining the respective area under each curve in step (f);

h) correlating the respective areas for each of at least two polymer training samples in step (g) with the known value of the respective physical or chemical property; and

i) applying the correlation of step (h) to the respective area of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample.

While not intended to be bound by this theory, Applicants believe that having more branches in the longer chains - the higher the molecular weight fraction - forces these chains into the amorphous region of the polymer and consequently increases the likelihood that they will act as interlaced molecules, maintaining semicrystalline polymeric matrix. These intertwined molecules can contribute significantly to improving the hardness properties (eg tear strength, impact, puncture or stress cracking) of polymers. In this aspect of the present invention, the above method is directed to determining the value of a physical or chemical property of a polymeric test sample using probabilities of entangled molecules.

This method of the present invention employs at least two polymeric training samples. Each polymeric training sample has a known composite density, a known MWD profile, and a known SCBD. As noted above, composite density can be determined by ASTM D 1238, while MWD profile and SCBD can be determined using SEC-FTIR, for example. For an exemplary polyolefin copolymer, Figure 1 illustrates the MWD and SCBD profile of the copolymer. Graphic data, as illustrated in Figure 1, may be provided for at least two polymeric training samples and at least one polymeric test sample. Also, each polymeric training sample has a known value of the respective physical or chemical property of interest. For example, at least two polymeric training samples may be provided, each having a known value of PENT at 2.4 MPa, the value of PENT having been previously determined using the respective analytical test for PENT.

At least two polymeric training samples are used in the methods of the present invention. Alternatively, however, at least three training samples, at least four training samples, at least five training samples, at least ten training samples, at least fifteen training samples or at least twenty training samples may be used. There is no specific upper limit on the number of different training samples that can be used with the present invention. It is beneficial that training samples resemble the polymeric test sample, and that the range covered by the training samples encompasses the polymeric test sample, although it is not required. In addition, training samples may include duplicate or redundant samples to include the impact of experimental error on testing for composite density, MWD and SCBD profile, and the respective physical or chemical property of interest.

For each of at least two polymeric training samples and at least one polymeric test sample, at least two respective density terms and molecular weights along the MWD and SCBD profile are determined using composite density, MWD profile and SCBD. In order to determine at least two terms of density, a relationship between density and molecular weight is used.

The composite density of a polymer may depend on, among other things, the MWD profile and the SCBD of the polymer. In one aspect of the present invention, each term of density is determined using an empirical correlation between composite density and molecular weight. For certain homopolymers such as high density polyethylene, the density of the composite decreases as molecular weight increases. Using a set of restricted MWD homopolymers (polydispersity index of about 2.3) as disclosed in Jordens et al., In "POLYMER", 41 (2000), 7175, an empirical correlation between composite density and molecular weight can be determined. Figure 4 illustrates a graph of composite density versus weighted average molecular weight logarithm for an exemplary high density polyethylene homopolymer. By applying this linear correlation between composite density and molecular weight logarithm to the exemplary MWD profile illustrated in Figure 1, the terms of density at respective molecular weights can be determined.

For copolymers with short chain branches or side chains that may still suppress density, a correlation may be applied to the correlation of Figure 4. The density terms derived from Figure 4 are adapted based on their respective weight fractions to estimate a calculated density without assuming short chain branches. For example, assuming a copolymer with a composite density of about 0.951 g / mL, the calculated density assuming no short chain branching may be about 0.957 g / mL, a difference of about 0.006 g / mL. A correlation factor, based on this change in composite density divided by the average number of SCBs in the SCBD, can then be applied to determine each density term for a copolymer. The average number of SCB's can be determined using analytical techniques such as NMR or SEC-FTIR. For the exemplary copolymer in Figure 1, the average number of SCB's across the entire polymer is about 1.5. Thus, on average, the density term at each molecular weight for this exemplary copolymer reduces about 0.004 g / mL (0.006 divided by 1.5) to each short-chain branch per 1,000 31/49 atoms.

carbon. For simplicity, this assumes, although not correctly, that each short-chain branch suppresses density equally at all SCB levels and at all molecular weights through the MWD profile. This process is illustrated in Figure 5 for the MWD profile. The upper line superimposed on the MWD profile in Figure 5 uses the density correlation of Figure 4 and assumes a homopolymer, ie no short chain branches The lower line used the correlation factor based on change in composite density divided by the average number of SCBs in the SCBD to determine density terms across the MWD profile for the copolymer From Figure 5, a term of copolymer density at each respective MW can be determined.

According to one aspect of the present invention, at least two terms of density at respective molecular weights along the MWD and SCBD profile are required. Although at least two terms of density are required, it is beneficial to have many more terms of density across the molecular weight range to form the curves and correlations illustrated in Figure 5. Thus, according to another aspect of the present invention, at least five terms. At least ten density terms, at least twenty-five density terms, at least fifty density terms or at least one hundred density terms may be used. There is no specific upper limit on the number of density terms that may be used with the present invention. More density terms can provide a more accurate correction factor and a more accurate copolymer density curve, as illustrated in Figure 5.

A respective melting temperature can then be determined from each density term. Such a method is the use of an empirical correlation between melt temperatures and density, such as those illustrated in Figure 6 for a polyethylene polymer. Data in this chart are from Patel et al., J. APPL. POLY. SCI 60 (1996), 749; Mirabella et al., J. POLY. SCI., PART B: POLYMER PHYSICS, 40 (2002), 1637; and Huang et al., J. POLY. SCI., PART B: POLYMER PHYSICS, 28 (1990), 2007. For curve fitting purposes, a point at a density of 1.01 g / mL was noted by the Requesters. Using fog 6, a melt temperature can be determined from each density term at a respective molecular weight through the MWD profile of Figure 5.

In one aspect of the present invention, from each melting temperature, a respective probability for interlaced molecule formation is determined. One technique involves determining at each respective MW the crystalline lamella thickness (Lc) and amorphous layer thickness (La) using the melting temperature of Figure 6 and the Gibbs-Thompson equation, which is readily known from that. of common skill in the technique. The goal is not only to determine Lc and La, but to determine 2LC + La at each respective MW. 2LC + La is generally understood to be the minimum molecule length for an interlaced molecule, where the interlaced molecule extends over the amorphous layer and extends over two crystalline lamellae. Figure 7 illustrates that the method of the present invention for determining 2LC + La (measured in nm) as a density function fits reasonably well with 2LC + La values reported in the literature of Patel et al., Mirabella et al. And Huang et al. . Some deviation from model prediction may be due to the fact that the reported values are at a molecular weight equal to Mw.

Since 2LC + La has been determined for each respective MW, the probability of interlaced molecule formation can be determined (abbreviated as P or PTm).

At each respective MW Ptm is the probability that a molecule will extend more than 2LC + La at this respective MW. Huang et al., J. MATERIAL SCI., 23 (1988), 3648, described a method for calculating the probability that a molecule of a particular molecular weight (Mw) would form an interlaced molecule across a 2LC + La distance using the following equation. :

<formula> formula see original document page 34 </formula>

The symbols above have the following meanings:

P = Probability of interlaced chain formation

L = Critical Distance = 2Lc + La

Lc = coverslip thickness

La = Amorphous layer thickness

D = Fusion Chain Extension Factor = 6.8 for polyethylene

η = Number of connections = Mw / 14 for polyethylene

1 = Bond length = 0.153 nm for polyethylene Spreadsheets and / or computer-based methods may be used to determine the P or Ptm value at each respective MW from the respective melt temperature. Calculated PTm values using the present method compare well with values reported in the literature, as by Patel et al. Some limitations of this method for determining PTm may include that Ptm alone does not reflect the concentration of actual entangled molecules in semicrystalline polymers (ie, entanglement turns may also serve as junction points). In addition, only static levels of entangled molecules are accounted for in these calculations and do not include new entangled (dynamic) strands that may be formed due to lamellar slip as a result of deformation.

For each of at least two polymeric training samples and at least one polymeric test sample, the weighted interlaced molecule probabilities can be determined using the respective data for each sample. A weighted interlaced probability is the product of multiplying the weight fraction at a respective molecular weight and the PTm / a probability for formation of intertwined molecules at the respective molecular weight (ie dW / d (Log M) * PTra) .

According to one aspect of the present invention, at least two probabilities of intertwined molecules weighted at respective molecular weights over the MWD profile and SCBD are required. Each probability of weighted entangled molecules is plotted versus the logarithm of their molecular weight for each of at least two polymeric training samples and at least one polymeric test sample. This is illustrated in Figure 8 for two exemplary polyolefin copolymers. While at least two probabilities of weighted entangled molecules are required, it is beneficial to have much more terms of probability across the molecular weight range to form the curve illustrated in Figure 8. Thus, according to another aspect of the present invention, at least five probabilities of weighted entangled molecules, at least ten probabilities of weighted entangled molecules, at least twenty five probabilities of weighted entangled molecules, at least fifty odds of weighted entangled molecules or at least one hundred odds of weighted entangled molecules can be used. There is no specific upper limit on the number of probabilities of weighted entangled molecules that can be used with the present invention. More probabilities of weighted interlaced molecules provide a smoother curve, as illustrated in Figure 8.

For each of the at least two polymeric training samples and at least one polymeric test sample, the area under the respective curve for each sample is determined. For example, the areas under the curves of Figure 8 for exemplary copolymers are determined.

The respective areas under the curve for each of at least two polymeric training samples correlate with the respective values of the physical or chemical properties of interest. In one aspect of the present invention, the area under each curve is multiplied by 100 to calculate primary structure parameter 2 (PSP2). In Figure 8, the polymer sample with the highest peak has a PSP2 value of 10.9, while the polymer sample with the smallest peak has a PSP2 value of 9.8.

Correlations with a specific physical or chemical property using at least two polymeric training samples can also be made with the value of PSP2.

By applying the correlation with the respective areas under the curves of at least one polymeric training sample to the respective area under the curve of at least one polymeric test sample, the value of the physical or chemical property of interest for at least one sample polymeric test can be determined. This method is further illustrated in the following Examples 6 to 8.

This method involving entangled molecules can be used when at least two polymeric training samples and at least one polymeric test sample are prepared using catalyst systems that are identical or different. For example, this method may be used for different families of polyolefin resins produced with different catalyst systems (such as chromium, Ziegler-Natta, metallocene and the like, or combinations thereof) or with different production processes (such as semifluid mixture, solution, gas phase and the like or combinations thereof).

Another aspect of the present invention provides a method for determining a physical or chemical property value of at least one polymeric test sample to at least one polymeric test sample having a composite density, molecular weight and weight fraction. at a respective molecular weight. These parameters can be determined by various analytical techniques known to those of ordinary skill in the art, as discussed above. This method for determining a physical or chemical property value of at least one polymeric test sample comprises:

(a) provide at least two training samples, each training sample having a composite density, molecular weight, molecular weight fraction and known physical or chemical property value;

b) determining a minimum molecule length for one interlaced molecule (2LC + La) using the composite density for each of at least two polymeric training samples and at least one polymeric test sample;

c) determining a respective probability for intertwined molecule formation at the respective molecular weight from each 2LC + La of step (b);

d) determining a probability of respective heavy entangled molecule, each probability of heavy entangled molecule being determined as the product of the multiplication of:

(1) the weight fraction of the respective molecular weight; and

(2) the probability for formation of entangled molecule in step (c) at the respective molecular weight;

e) correlating the respective probability of heavy entangled molecule for each of at least two polymer training samples in step (d) with the known value of the respective physical or chemical property; and

f) applying the correlation of step (e) to the probability of heavy entangled molecule of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample.

The above method is a single point determination of the method illustrated in Figures 4 to 8. In this method, a single probability of weighted interlaced molecule is determined at a single molecular weight for each of at least two polymeric training samples and at least a polymeric test sample. In this regard, the composite density reflects the impact of short chain branching and molecular weight across the entire polymer. Using the correlation illustrated in Figure 7, respective 2LC + La values can be determined from the respective composite density of the polymer sample. This method is further illustrated in Example 9 below.

EXAMPLES

EXAMPLE 1

Table 1 lists Mw, composite density and measured PENT (hours) at 2.4 MPa for seven (7) bimodal polyethylene polymers produced using Ziegler-Natta catalysts. Figures 9 to 15 are the MWD and SCBD profile of these seven polymeric training samples. These Figures illustrate measured data and adjusted SCBD using a SEC-FTIR technique as described in U.S. Patent No. 6,632,680 and U.S. Patent Application Serial No. 10 / 463,849. Due to the reduced weight fraction at very high molecular weights, it is often difficult to accurately measure SCBD's at these respective molecular weights. Application of the methodology discussed above with respect to the weighted cross-terms of these seven training samples resulted in the curves shown in Figure 16. The areas under the curves in Figure 16 decrease from the BM-I to BM-7 polyethylene polymer resin. Figure 17 illustrates that a strong linear correlation exists between the Log PENT and PSP1 value for these polymers. Since an exact PENT value was not established for polymer BM-1, it was not plotted in Figure 17. Thus, the PENT value of a test sample (an unknown and experimental sample) of the same polymer family The bimodal value could be determined by applying the correlation in Figure 17 to the PSP1 value of the test sample.

EXAMPLE 2

Five (5) unimodal polyethylene polymers were produced using chromium-based catalyst. These polymers had composite densities in the range of about 0.94 to about 0.950 and Mw in the range of about 260 to about 320 kg / mol. The PENT value at 2.4 MPa, the MWD profile and the SCBD of these five polymeric training samples were also provided. Although MWD and SCBD profile data are not shown, this information is exemplified in Figures 9 to 15 listed in Example 1. Application of the previously discussed weighted crossover methodology of these five samples resulted in the curves illustrated in Figure 18. Figure 19 illustrates that there is a strong linear correlation between the Log PENT and PSP1 value for these polymers. Thus, the PENT value of a test sample from the same polymer family could be determined by applying the correlation in Figure 19 to the PSP1 value of the test sample.

EXAMPLE 3

Example 3 shows the same bimodal polyethylene polymers discussed in Example 1. Table II lists a specific molecular weight, weight fraction at this molecular weight, SCB's at this molecular weight and measured PENT (hours) at 2.4 MPa for six. (6) bimodal polyethylene polymers. Weighted cross terms were weighted for one of these six training samples, divided by 100,000 and plotted against the measured PENT value. Even with this single-point method (ie, taking the data at only one molecular weight, Log M = 6.05), Figure 20 illustrates that there is a strong linear correlation between the Log PENT value and the divided weighted cross-term. per 100,000. Thus, the PENT value of a test sample from the same bimodal polymer family could be determined by applying the correlation in Figure 20 to a single weighted crossover term of the test sample.

EXAMPLE 4

Table III lists the predicted PENT value at 2.4 MPa using chemometric analysis against the measured PENT value for a series of polyethylene polymers produced using chrome, Ziegler-Natta and double catalyst systems. These data are graphically illustrated in Figure 21. The MWD profile and SCBD of these polymeric training samples were provided through SEC-FTIR. Although MWD and SCBD profile data are not shown, this information is exemplified in Figures 9 to 15 listed in Example 1. Weighted cross-terms along the MWD and SCBD profile were determined for each of the polymeric training samples. . Chemometric methods were used to generate a mathematical relationship, or correlation, between PENT values and weighted cross terms, and subsequently to PSP1. The mathematical relationship illustrated in Figure 21 was independent of the catalyst system and process used to produce the polymeric training samples. Thus, the PENT value of a test sample from the same polymer family could be determined by applying chemometric analysis to the PSP1 value of the test sample.

EXAMPLE 5

Table IV lists the predicted PENT value at 2.4 MPa using chemometric analysis against the measured PENT value for a series of polyethylene polymers produced using different catalyst systems. These data are graphically illustrated in Figure 22. The MWD profile and SCBD of these polymeric training samples were provided through SEC-FTIR. Although MWD and SCBD profile data are not shown, this information is exemplified in Figures 9 to 15 listed in Example 1. Weighted cross-terms along the MWD and SCBD profile were determined for each of the polymeric training samples. . Chemometric methods were used to generate a mathematical relationship, or correlation, between PENT values and weighted cross terms, and subsequently to PSP1. The mathematical relationship illustrated in Figure 22 was independent of the catalyst system and process used to produce the polymeric training samples. Thus, the PENT value of a test sample from the same polymer family could be determined by applying chemometric analysis to the PSP1 value of the test sample.

EXAMPLE 6

In this example, two different families of polymers were evaluated. Five (5) unimodal polyethylene polymers produced using chromium-based catalyst were selected. These polymers had a large MWD; The average polydispersity index for the five polymers was about 30. Six (6) bimodal polyethylene polymers produced using Ziegler-Natta catalysts were selected. These bimodal polymers had an average polydispersity index of about 17. The PENT value at 2.4 MPa, the MWD profile and the SCBD of these eleven polymeric training samples were provided. Although MWD and SCBD profile data are not shown, this information is exemplified in Figures 9 to 15 related to Example 1. Composite densities were provided and ranged from about 0.947 to about 0.957 g / mL for the eleven samples. polymeric training The application of the methodology discussed above with respect to the probabilities of weighted entangled molecules in these eleven training samples resulted in curves similar to those exemplified in Figure 8. The respective areas under the curves were determined and multiplied by 100 to calculate the respective PSP2 value for each. training sample. Figure 23 illustrates that there is a strong linear correlation between the Log PENT and PSP2 value for these polymers, regardless of the catalyst system used to produce the polymeric training samples. Thus, the PENT value of a polymeric test sample using similar or different catalyst systems could be determined by applying the correlation in Figure 23 to the PSP2 value of the test sample.

EXAMPLE 7

In this example, three different families of polymers were evaluated: unimodal polyethylene polymers produced using a chrome-based catalyst and polymers produced using Ziegler-Natta catalysts, and bimodal polyethylene polymers produced using Ziegler-Natta catalyst. The SP-NCTL value, MWD profile and SCBD of these fifteen (15) polymeric training samples were provided. Although MWD and SCBD profile data are not shown, this information is exemplified in Figures 9 to 15 related to Example 1. Composite densities were provided and ranged from about 0.93 to about 0.96 g / mL. for the fifteen polymeric training samples. The application of the methodology discussed above with respect to the probabilities of weighted entangled molecules of these eleven training samples resulted in curves similar to those exemplified in Figure 8. The respective areas under the curves were determined and multiplied by 100 to calculate the respective PSP2 value for each. training sample. Figure 24 illustrates that there is a strong linear correlation between the Log SP-NCTL and PSP2 value for these copolymers, regardless of the catalyst system used to produce the polymeric training samples. In addition, these polymers embraced a wide range of composite density. Thus, the SP-NCTL value of a polymeric test sample using similar or different catalyst systems could be determined by applying the correlation in Figure 24 to the PSP2 value of the test sample.

EXAMPLE 8

In this example, five different families of polymers were evaluated: unimodal polyethylene polymers produced using a chromium-based catalyst, Ziegler-Natta catalysts and metallocene catalysts; and bimodal polyethylene polymers produced using Ziegler-Natta catalysts and metallocene catalysts. Typical applications for these polymeric resins include, but are not limited to, blow molding, tubing, geomembrane and film applications. The NDR value, MWD profile and SCBD of these thirty-eight (38) polymeric training samples were provided. Although MWD and SCBD profile data are not shown, this information is exemplified in Figures 9 to 15 related to Example 1. Composite densities were provided and ranged from about 0.91 to about 0.96 g / mL. for the thirty eight (38) polymeric training samples. The application of the methodology discussed above with respect to the probabilities of weighted entangled molecules of these thirty-eight training samples resulted in curves similar to those exemplified in Figure 8. The respective areas under the curves were determined and multiplied by 100 to calculate the respective PSP2 value. for each training sample. Figure 25 illustrates that there is a strong linear correlation between the NDR and PSP2 value for these polymers, regardless of the catalyst system used to produce the polymeric training samples. In addition, these polymers have embraced a wide range of composite density and are used in a wide variety of end user applications. Thus, the NDR value of a polymeric test sample using similar or different catalyst systems could be determined by applying the correlation in Figure 25 to the PSP2 value of the test sample.

EXAMPLE 9

Example 1 uses the same bimodal polyethylene polymers discussed in Example 1. Table V lists a specific molecular weight, weight fraction at this molecular weight, composite density and measured PENT (hours) at 2.4 MPa for six ( 6) bimodal polyethylene polymers. The 2LC + La values were determined and the weighted interlaced molecule probabilities were calculated for each of these six training samples. The Log PENT value was plotted against the weighted interlaced molecule probabilities, as shown in Figure 26. Even with this single-point method (ie, taking the data only at one molecular weight, Log M = 5.7), the Figure 26 illustrates that there is a strong linear correlation between the Log PENT value and the probability of weighted interlaced molecule. Thus, the PENT value of a test sample from the same bimodal polymer family could be determined by applying the correlation in Figure 26 to a single weighted interlaced molecule probability of the test sample.

Table 1. Bimodal Polyethylene Polymer Data

<table> table see original document page 47 </column> </row> <table>

Table 2. Single molecular weight bimodal polyethylene polymer data

<table> table see original document page 47 </column> </row> <table>

Table 3. Predicted PENT (h) using Chemometric Analysis against PENT (h) Measured

<table> table see original document page 47 </column> </row> <table> <table> table see original document page 48 </column> </row> <table>

Table IV. PENT (h) Predicted using Measured PENT Chemistry Analysis (h)

<table> table see original document page 48 </column> </row> <table> <table> table see original document page 49 </column> </row> <table>

Table V. Single molecular weight bimodal polyethylene polymer data

<table> table see original document page 49 </column> </row> <table> <table> table see original document page 50 </column> </row> <table>

Claims (38)

1. Method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a molecular weight distribution (MWD) profile and a short chain branch distribution ( SCBD), characterized in that it comprises: a) providing at least two training samples, each training sample having a MWD profile, an SCBD and a known value of the respective physical or chemical property; b) determining at least two cross-weighted terms at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each weighted cross-term being determined as the product of multiplication of: (1) its molecular weight; (2) the weight fraction of the respective molecular weight; and (3) the number of short chain branches per -1,000 carbon atoms at the respective molecular weight; c) plotting each weighted cross-term versus molecular weight logarithm for each of at least two polymer training samples and at least one polymeric test sample; d) determining the respective area under each curve in step (c); e) correlating the respective areas for each of at least two polymer training samples in step (d) with the known value of the respective physical or chemical property; and f) applying the correlation of step (e) to the respective area of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample. Method according to claim 1, characterized in that the physical or chemical property is PENT at 2.4 MPa. Method according to claim 1, characterized in that the physical or chemical property is PENT at 3.8 MPa. Method according to claim 1, characterized in that the physical or chemical property is Environmental Stress Crack Resistance (ESCR). Method according to claim 1, characterized in that the physical or chemical property is Single Point Grooved Constant Tensile Load (SP-NCTL). Method according to claim 1, characterized in that the physical or chemical property is Grooved Tube Test (NPT). Method according to claim 1, characterized in that the physical or chemical property is Complete Splined Fluency Test (FNCT). Method according to claim 1, characterized in that the physical or chemical property is Natural Breath Ratio (NPT). Method according to claim 1, characterized in that the MWD profile and SCBD are obtained from SEC-FTIR analysis. A method according to claim 9, characterized in that less than about 1 gram of each of at least two polymeric training samples and at least one polymeric test sample is provided for analysis. Method according to claim 1, characterized in that the area under the curve in step (d) is divided by 100,000 to calculate the primary structure parameter 1 (PSP1). Method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a MWD profile and an SCBD, comprising: a) providing at least two training samples, each training sample having a MWD profile, an SCBD and a known value of the respective physical or chemical property; b) determining at least two cross-weighted terms at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each weighted cross-term being determined as the product of multiplication of: (1) its molecular weight; (2) the weight fraction of the respective molecular weight; and (3) the number of short chain branches per -1,000 carbon atoms at the respective molecular weight; c) by chemometric analysis, define a mathematical relationship between the values of the respective physical or chemical property and the weighted cross terms for each of at least two polymeric training samples; and d) applying the mathematical relationship of step (c) to the respective weighted cross-terms of step (b) for at least one polymeric test sample to determine the physical or chemical property value of at least one polymeric test sample. Method according to claim 12, characterized in that the physical or chemical property has a PENT value of 2.4 MPa. Method according to claim 12, characterized in that the physical or chemical property has a PENT value of 3.8 MPa. A method according to claim 12, characterized in that the physical or chemical property is Environmental Stress Crack Resistance (ESCR). A method according to claim 12, characterized in that the physical or chemical property is Single Point Grooved Constant Tensile Load (SP-NCTL). Method according to claim 12, characterized in that the physical or chemical property is Grooved Pipe Test (NPT). The method according to claim 12, characterized in that the physical or chemical property is Complete Splined Fluency Test (FNCT). A method according to claim 12, characterized in that the physical or chemical property is Natural Breath Ratio (NPT). Method according to claim 12, characterized in that the MWD profile and SCBD are obtained from SEC-FTIR analysis. A method according to claim 20, characterized in that less than about 1 gram of each of the at least two polymeric training samples and at least one polymeric test sample is provided for analysis. Method according to claim 12, characterized in that the at least two polymeric training samples and at least one polymeric test sample are prepared using catalyst systems that are the same or different. 23 Method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a composite density, a MWD profile and an SCBD, comprising: provide at least two training samples, each training sample having a composite density, a MWD profile, an SCBD and a known value of the respective physical or chemical property; b) determining at least two terms of density at respective molecular weights along the MWD and SCBD profile for each of at least two polymer training samples and at least one polymer test sample each density term. being determined using composite density, MWD profile and SCBD; c) determining a respective melting temperature from each density term in step (b); d) determining a respective probability for intertwined molecule formation from each melting temperature in step (c); e) determining a respective weighted interlaced molecule probability, each weighted interlaced molecule probability being determined as the product of the multiplication of: (1) the weight fraction of the respective molecular weight; and (2) the probability for formation of entangled molecule in step (d) at the respective molecular weight; f) plotting each probability of weighted entangled molecule versus molecular weight logarithm for each of at least two polymer training samples and at least one polymeric test sample; g) determining the respective area under each curve in step (f); h) correlating the respective areas for each of at least two polymer training samples in step (g) with the known value of the respective physical or chemical property; and i) applying the correlation of step (h) to the respective area of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample. A method according to claim 23, characterized in that the physical or chemical property has a PENT value of 2.4 MPa. Method according to claim 23, characterized in that the physical or chemical property has a PENT value of 3.8 MPa. A method according to claim 23, characterized in that the physical or chemical property is Environmental Stress Crack Resistance (ESCR). A method according to claim 23, characterized in that the physical or chemical property is Single Point Grooved Constant Tensile Load (SP-NCTL). A method according to claim 23, characterized in that the physical or chemical property is Grooved Tube Test (NPT). A method according to claim 23, characterized in that the physical or chemical property is Complete Splined Fluency Test (FNCT). A method according to claim 23, characterized in that the physical or chemical property is Natural Breath Ratio (NPT). Method according to claim 23, characterized in that the MWD profile and SCBD are obtained from SEC-FTIR analysis. A method according to claim 31, characterized in that less than about 1 gram of each of the at least two polymeric training samples and at least one polymeric test sample is provided for analysis. A method according to claim 23, characterized in that the at least two polymeric training samples and at least one polymeric test sample are prepared using catalyst systems that are the same or different. The method according to claim 23, characterized in that the area under the curve in step (g) is multiplied by 100 to calculate the primary structure parameter 2 (PSP2). A method according to claim 23, characterized in that each density term of step (b) is determined using an empirical correlation between composite density and molecular weight and a correction factor based on a change in density. composite density divided by the average number of short chain branches per 1,000 carbon atoms in the SCBD. The method according to claim 23, characterized in that each melting temperature of step (c) is determined using an empirical correlation of melting temperature with density. 37. Method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a molecular weight, a weight fraction at its molecular weight and a number of chain branches. short by 1,000 carbon atoms in their molecular weight, comprising: a) providing at least two polymeric training samples, each training sample having a molecular weight, a fraction of weight at its molecular weight, a number of branches of short chain per 1,000 carbon atoms at their molecular weight and a known value of their physical or chemical property. (b) determine a weighted cross-term in its molecular weight for each of at least two polymeric training samples and at least one polymeric test sample, each weighted cross-term being determined as the product of multiplication of: (1) the respective molecular weight; (2) the weight fraction of the respective molecular weight; and (3) the number of short chain branches per -1,000 carbon atoms at the respective molecular weight; c) correlating the respective weighted cross terms for each of at least two polymer training samples in step (b) with the known value of the respective physical or chemical property; and d) applying the correlation of step (c) to the weighted cross-term of at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample. 38. Method for determining a physical or chemical property value of at least one polymeric test sample, at least one polymeric test sample having a composite density, molecular weight and weight fraction at respective molecular weight, characterized in comprising: (a) providing at least two training samples, each training sample having a composite density, molecular weight, molecular weight fraction and known value of the respective physical or chemical property; b) determining a minimum molecule length for one interlaced molecule (2LC + La) using the composite density for each of at least two polymeric training samples and at least one polymeric test sample; c) determining a respective probability for intertwined molecule formation at the respective molecular weight from each 2LC + La of step (b); d) determining a probability of respective weighted entangled molecule, each probability of weighted entangled molecule being determined as the product of multiplication of: (1) the weight fraction of the respective molecular weight; and (2) the probability for formation of entangled molecule in step (c) at the respective molecular weight; e) correlating the respective probability of weighted entangled molecule for each of at least two polymer training samples in step (d) with the known value of the respective physical or chemical property; and f) applying the correlation of step (e) to the weighted entangled probability of the at least one polymeric test sample to determine the physical or chemical property value of the at least one polymeric test sample.